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Improved asymptotic stability analysis for uncertain delayed state neural networks

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  • Souza, Fernando O.
  • Palhares, Reinaldo M.
  • Ekel, Petr Ya.

Abstract

This paper presents a new linear matrix inequality (LMI) based approach to the stability analysis of artificial neural networks (ANN) subject to time-delay and polytope-bounded uncertainties in the parameters. The main objective is to propose a less conservative condition to the stability analysis using the Gu’s discretized Lyapunov–Krasovskii functional theory and an alternative strategy to introduce slack matrices. Two computer simulations examples are performed to support the theoretical predictions. Particularly, in the first example, the Hopf bifurcation theory is used to verify the stability of the system when the origin falls into instability. The second example is presented to illustrate how the proposed approach can provide better stability performance when compared to other ones in the literature.

Suggested Citation

  • Souza, Fernando O. & Palhares, Reinaldo M. & Ekel, Petr Ya., 2009. "Improved asymptotic stability analysis for uncertain delayed state neural networks," Chaos, Solitons & Fractals, Elsevier, vol. 39(1), pages 240-247.
    • Handle: RePEc:eee:chsofr:v:39:y:2009:i:1:p:240-247
    DOI: 10.1016/j.chaos.2007.01.110
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    References listed on IDEAS

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    1. Cao, Jinde & Ho, Daniel W.C., 2005. "A general framework for global asymptotic stability analysis of delayed neural networks based on LMI approach," Chaos, Solitons & Fractals, Elsevier, vol. 24(5), pages 1317-1329.
    2. Arik, Sabri, 2005. "Global robust stability analysis of neural networks with discrete time delays," Chaos, Solitons & Fractals, Elsevier, vol. 26(5), pages 1407-1414.
    3. Zhang, Qiang & Wei, Xiaopeng & Xu, Jin, 2005. "Delay-dependent exponential stability of cellular neural networks with time-varying delays," Chaos, Solitons & Fractals, Elsevier, vol. 23(4), pages 1363-1369.
    4. Singh, Vimal, 2007. "Improved global robust stability criterion for delayed neural networks," Chaos, Solitons & Fractals, Elsevier, vol. 31(1), pages 224-229.
    5. Singh, Vimal, 2006. "Simplified LMI condition for global asymptotic stability of delayed neural networks," Chaos, Solitons & Fractals, Elsevier, vol. 29(2), pages 470-473.
    6. Park, Ju H., 2006. "On global stability criterion for neural networks with discrete and distributed delays," Chaos, Solitons & Fractals, Elsevier, vol. 30(4), pages 897-902.
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    1. Souza, Fernando O. & Palhares, Reinaldo M. & Ekel, Petr Ya., 2009. "Novel stability criteria for uncertain delayed Cohen–Grossberg neural networks using discretized Lyapunov functional," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2387-2393.
    2. Kalpana, M. & Balasubramaniam, P. & Ratnavelu, K., 2015. "Direct delay decomposition approach to synchronization of chaotic fuzzy cellular neural networks with discrete, unbounded distributed delays and Markovian jumping parameters," Applied Mathematics and Computation, Elsevier, vol. 254(C), pages 291-304.

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